Let f be a $$real-valued$$ invertible function such that f $$2x-3x-2$$ $$=5x-2$$, x≠$$2$$. Then the value of $$f-1(13)$$ is

We have f $$2x-3x-2$$ $$=5x-2$$ ⇒$$f-1(5x-2)=2x-3x-2$$ let $$5x-2=13$$ then $$x=3$$ hence $$f-1(13)=2(3)-33-2=3$$

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Question

$Let f be a real-valued invertible function such that f (\frac{2 x - 3}{x - 2}) = 5 x - 2, x \neq 2 . T h e n t h e v a l u e o f f^{- 1} (13) i s$

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Solution

$We have f (\frac{2 x - 3}{x - 2}) = 5 x - 2 \Rightarrow f^{- 1} (5 x - 2) = \frac{2 x - 3}{x - 2} l e t 5 x - 2 = 13 t h e n x = 3 h e n c e f^{- 1} (13) = \frac{2 (3) - 3}{3 - 2} = 3$

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